20:31 Till. 26% Tshwane University of Technology We empower people FACULTY OF HUMANITIES DEPARTMENT OF MATHEMATICS, SCIENCE AND BUSINESS EDUCATION FMS206P & FTH206P TUTORIAL: Limits and Continuity QUESTION 1 1.1 Evaluate the following: sin 3x 1.1.1 lim x-0x(5x2 – 4) x²-81 1.1.2 lim x-9 x 9 1.1.3 lim X-100 5x - x2 -1 2x3-4x x²+9-3 1.1.4 lim QUESTION 2 2.1 State the Squeeze Theorem. 2.2 Suppose that the inequality April 2024 1 x2 - cos x 1 2 24 holds for all values of x close to zero. Find lim x-0 2.3 Determine the following limit by using the Squeeze Theorem QUESTION 3 lim 3x2 sin x0 3.1 State the epsilon-delta (ε - 6) definition of limit of a function. 3.2 Consider the limit lim (2x-1) = 7. 3.2.1 Use the epsilon-delta (-8) definition of a limit to prove that lim (2x-1)=7 Page 1 of 2 B x-4 3.2.2 How close to x₁ = 4 does x have to be so that y = 2x - 1 differ from 7 by less than 2 units? QUESTION 4

Q: x² - 9 lim x-3 x-3

A: As per the guidelines we can not proved the hand written solution. limx→3x2-9x-3 factorize the…

Q: sin 04) find limx-2n 2x-4n S0 (x²+x+1)* Q5) lim- (r²+1)100

A: In the given question we have to find the limit of the question 4 and question 5. the question 4 is…

Q: 3.) lim r/2

A: To find the limit of the function

Q: 1-3x limx-0 V5x2+2 Select one: О а. 5 -3 O b. 5 C. O d. 5 O e. none

A: Divide both numerator and denominator by x and use the limit

Q: sec 2X find the lim

A: To evaluate the limit: limx→0sec2x3x csc2x Solution: We know that, cscθ=1sinθ limx→0sinaxax=1…

Q: eed help thx

A:

Q: 1.) Evaluate each of the following limits. a.) lim (x2-3x + 1) x-2 x-1 b.) lim x-1x²-1

A: (a)  To compute     L = limx→-2x2-3x+1  Then we have L = -22-3-2+1

Q: Find the limnit L. X - 3 1. lim X4 X- 4

A:

Q: 2. lim (5* +x)×

A:

Q: x2-4 lim x--2 x2+4x+4

A: In this question, we have to find the limit of a function which is of the form 0/0.

Q: x? — х - 2 lim х->-1 x? + 3x + 2 X→-1

A:

Q: Tim X90 χε -3x

A: given limit

Q: Find the limits of the functions lim メ>- (6lim x 2. xペー 2x+4

A:

Q: 22- iz lim 23 +1 10 -1 0 20 00

A:

Q: ■ Find the limit.

A: Evaluate limx→∞3x-22x+1

Q: Lim 3-x Ix-31

A:

Q: + 75 3-4x Evaluate lim x-4 1 -4x-6 + Enter an exact answer. Provide your answer below: 13

A:

Q: x+5 -lim x-5 r²+25,

A: Given limit, limx→5x+5x2+25

Q: X 3 Solve for the lim 2-9 r+3 x2-9

A: Given that: limx→31x-13x2-9

Q: 22-7x 18 lim r -2 x + 2

A: Consider the following limit:…

Q: example Lim X-70 W. Inx UX

A:

Q: 2x Evaluate lim 1+

A:

Q: 3-x2 b. lim x→00 2x2+1

A:

Q: x2-x-6 lim x-2 x2-4 Vx+2-2 lim x-2 x-2 Vk+3-V3 lim k-0 k

A:

Q: 4nx tan(- an %3D 7 + 16n lim an

A:

Q: Compute the limit. Justify your answer. 5x3-12x2+38x4– 19 lim 28x+19x-58x2-7 X- 00

A:

Q: (hi2-12th) h tth) hchtf2 H2th ) lim |

A:

Q: lim

A:

Q: - 36 73. lim x-6

A:

Q: 1\ x² – 12 x + 6 / 2х + 8 lim

A: To evaluate: limx→-62x+8x2-12-1xx+6